ODE
\[ \left (x^2+1\right ) y''(x)-2 y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0232831 (sec), leaf count = 30
\[\left \{\left \{y(x)\to c_1 \left (x^2+1\right )+\frac {1}{2} c_2 \left (\left (x^2+1\right ) \tan ^{-1}(x)+x\right )\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) = \left ( \left ( {\frac {x}{2\,{x}^{2}+2}}+{\frac {\arctan \left ( x \right ) }{2}} \right ) {\it \_C1}+{\it \_C2} \right ) \left ( {x}^{2}+1 \right ) \right \} \] Mathematica raw input
DSolve[-2*y[x] + (1 + x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (1 + x^2)*C[1] + ((x + (1 + x^2)*ArcTan[x])*C[2])/2}}
Maple raw input
dsolve((x^2+1)*diff(diff(y(x),x),x)-2*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = ((1/2*x/(x^2+1)+1/2*arctan(x))*_C1+_C2)*(x^2+1)